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This paper is concerned with the global asymptotic stability of the zero solution of the half-linear differential system $$x^{\text{'}}=-e\left(t\right)x+f\left(t\right){\phi }_{p^{*}}\left(y\right),y^{\text{'}}=-g\left(t\right){\phi }_p\left(x\right)-h\left(t\right)y,$$ where $p>1$, $p^{*}>1$ ($1/p+1/p^{*}=1$), and ${\phi }_q\left(z\right)={\left|z\right|}^{q-2}z$ for $q=p$ or $q=p^{*}$. The coefficients are not assumed to be positive. This system includes the linear differential system ${𝐱}^{\text{'}}=A\left(t\right)𝐱$ with $A\left(t\right)$ being a $2\times 2$ matrix as a special case. Our results are new even in the linear case ($p=p^{*}=2$). Our results also answer the question whether the zero solution of the linear system is asymptotically stable even when Coppel’s condition does not hold...